I have an Arduino Uno board. I made a digital clock using 16x2 lcd in 4 bit mode.It worked fine but thenI tried it to power it via an Ac to Dc adaptor of12V output conneted to domestic circuit(my house).At that moment I realised that the lcd was running much brighter and after few seconds the lcd display went crazy. Then I pulged it back to my Laptop to do some changes in my program.When i clicked "upload", error message occurred and it read that board was not connected. "ON" light is on but the built-in led is not blinking when I try to reset or reconnect the board.I tried different ports and even switched to another laptop but nothing changed.I had an acrylic case on the board se I can't tell if it was running hot or so. I assume you guys are much more experienced so Please help me ,This was my first project and I am kind of confused if the board could be used ever again. Also if this would have something to do with my code then reply to me and I will post the last code that I had uploaded to the board.

It may not be the answer you were looking for but its the one I am giving based on either experience, educated guess, google or the fact that you gave nothing to go with in the first place so I used my wonky crystal ball.

I wondered to different forums and someone wrote that connecting powerjack while usb is pluged could have caused the damage. But then there was a conflict among them saying that Arduino would automatically switch its power source.

Did pluging power jack and usb simultaneously would have had caused the damage !?, If yes ,damaged what, can it be repaired/replaced ?

It is necessary to just have patience. A lot of people reading may not know what advice to give, so they just move on to another topic, which may be something they know about. There may be a few that know about your topic.

Here is my suggestion. Disconnect the Uno from your project, and connect it with the USB cable to your computer. Carefully feel with your finger the various chips on the Uno to see if any of them are hot or warm to the touch. If they do get hot, then replace the Uno.

If it is running cool, there is a chance that the USB-to-serial chip or the main processor may have lost their bootloader or programming due to the voltage abuse that the Uno was exposed to. There is a chance, but no guarantee, that you could use a programmer or another Arduino loaded with the Arduino as ISP sketch, to bootload the main processor and re-program the main USB-to-serial prog. Only some Unos use the ATmega16u2 as the USB-to-serial chip, and those are the ones that are re-programmable. Unos with CH340G or FT232R chips are not re-programmable. All Unos have the main processor ATmega328P which can be re-bootloaded.

If your Uno has parts that get warm, I recommend putting it in a boneyard box with a note taped to it that says it is for parts. When you gain more experience, you may be able to take parts off of it to use in other projects, or may be able to revive it.

I wondered to different forums and someone wrote that connecting powerjack while usb is pluged could have caused the damage. But then there was a conflict among them saying that Arduino would automatically switch its power source.

Did pluging power jack and usb simultaneously would have had caused the damage !?, If yes ,damaged what, can it be repaired/replaced ?

You can connect it to external power at the same time as USB, but I recommend powering it at the power jack with no more than 9VDC, and use a volt meter to check because there are so many unregulated junk power supplies out there in the world that are just not very good. The regulator onboard the Uno that converts the 7 to 12V input power to regulated 5V is inefficient and on many Unos the regulator has a max input of 12V, so if you're power supply was above 12V it could cause problems. [EDIT: the Uno regulator has a max input voltage of 20V, but the bigger the difference between the input voltage and the 5V that the regulator is trying to output, the more heat the regulator must dissipate, and the Uno does not have a heat sink on the regulator. So it is more reasonable to input 9V max]. To externally power an Uno, you may want to use a USB phone charger, such as one for an iPhone, and a USB cable. Those usually have better power regulation.